Don't think about your bet size in terms of BB's after the flop. You want to bet keeping the size of the pot in mind. So your 3x bb bet on the flop was, assuming UTG limped and you checked which is what I think you meant, a good size. Assuming there were antes at this stage you bet probably like 75% of the pot. Which is standard and good, cause you want a caller at this point.
Now on the turn, the board paired. That's a little bit of a scare card for you, you led out on the flop and he called, so you have to think he has at least a pair at this point. You are way ahead at this point or way behind. So I would check here, if he had top pair he now has trips, if he limped UTG with something weird like 97 or 96 suited he could have a full house or if he had 66 or 77 he also has a FH or 99 for quads. I would think the pp's are more likely than the suited connectors. He could have slow played a big PP too, like AA or KK. So again, you are way ahead or way behind. So checking here with the intention of calling a pot size bet would be the play I would make. If he has the FH he will probably bet for value, which we will call to see the river. If he has an over pair like AA, the 9 on the turn might have scared him, becasue we did lead out on the flop, so he will probably check. If he had top pair, he now has trips and will probably bet for value, cause your straight draw is hidden here. And due to the board we know he's not on a flush draw.
So lets say he bets the turn, and we call. River card is another crappy card for us. The board is paired twice. Now if he had top pair he has a full house, and if he had 66 he has a FH, but the lowest possible FH. Or he could have quad sevens. So there is pretty much no way you can bet this river, you have to check here. Now if he moves all in there is no way we can call here, we have to fold. An all in bet here would look like he is bluffing, but that's all we are beating is a bluff. We still have a healthy stack and plenty of time for better spots, so if he wants to bluff us here, we have to let him have it.
At these limits players don't really know what bet sizing is. They don't really know how to suck every chip out of their opponent for value. So a lot of the times an all in bet on the river pretty much means they have the nuts. A pot size bet could mean I have an over PP, but the board scares me a little so I'll bet the pot. This could also be a value bet. So you are getting two to one to call, you need to think about the opponent and would he bet the pot there as a bluff, it's cheap enough to look him up, but it also smells fishy. So I'm still folding most of the time, unless I have a really good read on this player.
If he is a really good player he will price you into call, giving you three to one or four to one to call. This is almost two good to pass up, which is usually a red flag that it's a value bet. However, at these limits not a lot of the players are really thinking on that level. I will usually make the call with pot odds
of three to one at these limits and almost always make the call with four to one pot odds
. This is probably a leak in my game, but again most of the players at this level aren't thinking about pot odds and value betting the river. I'm surprised when i make that call, how often I win the hand. I need to look at some data to see if I'm winning overall making that call. I'm just not sure how to look at that in PT3. If I do I will post some numbers.
So I kinda rambled on here, but I hope that makes sense to you on why I would play it that way. search CC for way ahead way behind, there are some good articles on it. By playing the hand this way you still lose in this situation, but you still have most of your stack left.